GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Jun 2018, 21:51

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M06-16

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46214
M06-16 [#permalink]

Show Tags

New post 16 Sep 2014, 00:27
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

47% (01:04) correct 53% (01:18) wrong based on 174 sessions

HideShow timer Statistics

If \(\frac{t}{u} = \frac{x}{y}\) and \(\frac{t}{y} = \frac{u}{x}\) and \(t\), \(u\), \(x\), and \(y\) are non-zero integers, which of the following is true?

A. \(\frac{t}{u}=1\)
B. \(\frac{y}{x}=-1\)
C. \(t = -u\)
D. \(t = \pm u\)
E. None of the above

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46214
Re M06-16 [#permalink]

Show Tags

New post 16 Sep 2014, 00:27
1
5
Official Solution:

If \(\frac{t}{u} = \frac{x}{y}\) and \(\frac{t}{y} = \frac{u}{x}\) and \(t\), \(u\), \(x\), and \(y\) are non-zero integers, which of the following is true?

A. \(\frac{t}{u}=1\)
B. \(\frac{y}{x}=-1\)
C. \(t = -u\)
D. \(t = \pm u\)
E. None of the above


Given that: \(\frac{t}{u} = \frac{x}{y}\) and \(\frac{t}{y} = \frac{u}{x}\).

So, \(\frac{t}{u} = \frac{x}{y}\) and \(\frac{t}{u} = \frac{y}{x}\) (from 2), which means that \(\frac{t}{u}\) and \(\frac{x}{y}\) equal to their reciprocals: \(\frac{t}{u}=\frac{u}{t}\) and \(\frac{x}{y}=\frac{y}{x}\). So, \(t^2=u^2\) and \(t^2=u^2\), which gives \(|t|=|u|\) (or which is the same \(t = \pm u\)) and \(|x|=|y|\) (or which is the same \(x = \pm y\)).


Answer: D
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Manager
Manager
User avatar
Joined: 03 Oct 2014
Posts: 138
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)
Reviews Badge
Re: M06-16 [#permalink]

Show Tags

New post 13 Feb 2015, 22:18
1
Eqn 1....Let t/u = x/y = k

Therefore t = uk, x = yk.....

Substitute in eqn 2...t/y = u/x

uk/y = u/yk

k^2 = 1

k = +/-1

so t = +/- u
Manager
Manager
avatar
Joined: 27 Jan 2013
Posts: 175
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT 1: 730 Q49 V40
GPA: 3.5
WE: Supply Chain Management (Telecommunications)
GMAT ToolKit User
Re: M06-16 [#permalink]

Show Tags

New post 17 Feb 2015, 11:55
Bunuel In questions where they ask which is true.. are they asking for must be true or which can be true?

Asking since i solved this question as which can be true and stopped after choosing A as A was coming as true for a case where all numbers were equal.
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46214
Re: M06-16 [#permalink]

Show Tags

New post 17 Feb 2015, 11:57
1
qw1981 wrote:
Bunuel In questions where they ask which is true.. are they asking for must be true or which can be true?

Asking since i solved this question as which can be true and stopped after choosing A as A was coming as true for a case where all numbers were equal.


Which is true = which must be true.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 05 Dec 2013
Posts: 29
Reviews Badge
Re: M06-16 [#permalink]

Show Tags

New post 10 Jun 2015, 11:54
Why are we cross-multiplying ? The question does not state that integers t,x,u,v are positive...
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46214
Re: M06-16 [#permalink]

Show Tags

New post 10 Jun 2015, 11:56
Intern
Intern
avatar
Joined: 18 Oct 2015
Posts: 2
GMAT 1: 720 Q47 V41
GPA: 3.98
Re: M06-16 [#permalink]

Show Tags

New post 11 Dec 2015, 05:31
Hi,

I did the following:

From (1), ty=xu (cross multiplying)
From (2), tx=uy

so adding each side of the equalities, t(x+y)=u(x+y) so t=u (and not t= +-u)

What am I doing wrong?
Manager
Manager
avatar
B
Joined: 16 Feb 2016
Posts: 53
Concentration: Other, Other
GMAT ToolKit User Premium Member Reviews Badge
Re: M06-16 [#permalink]

Show Tags

New post 26 Apr 2016, 18:39
m9338 wrote:
Hi,

I did the following:

From (1), ty=xu (cross multiplying)
From (2), tx=uy

so adding each side of the equalities, t(x+y)=u(x+y) so t=u (and not t= +-u)

What am I doing wrong?


t=u
would be true for negative and positive values of u.
But I can see that some people would choose E.
1 KUDOS received
Intern
Intern
avatar
B
Joined: 20 Jul 2012
Posts: 18
Reviews Badge
Re: M06-16 [#permalink]

Show Tags

New post 15 Jun 2016, 02:34
1
m9338 wrote:
Hi,

I did the following:

From (1), ty=xu (cross multiplying)
From (2), tx=uy

so adding each side of the equalities, t(x+y)=u(x+y) so t=u (and not t= +-u)

What am I doing wrong?



One explanation that i can offer here is as follows -

The equation t(x+y)=u(x+y) holds good in almost all case, however (given x,y are non zero integers), consider a scenario where x= -y.
In this case you cannot say that t=u as you cant divide both sides with (x+y) !!! why? coz its 0 :)

Incidentally this is one of the wrong answer choices as well
Intern
Intern
avatar
B
Joined: 21 Oct 2014
Posts: 4
Location: Ukraine
GMAT 1: 680 Q48 V35
GPA: 3.05
GMAT ToolKit User
Re: M06-16 [#permalink]

Show Tags

New post 18 Feb 2017, 07:53
I still can't understand why option D is correct, even though the question is MUST BE TRUE.
Here is my thinking:

Let's say t, u, x and y are all equal to 1 (non-zero integer). Then according to option D: 1 = +-1, which is only true for positive sign, but not negative. I mean the option D would be a MUST BE TRUE answer only if it was written like this:
t = u OR t = -u.
As far as I understand t = +-u means 't = u AND t = -u'
Re: M06-16   [#permalink] 18 Feb 2017, 07:53
Display posts from previous: Sort by

M06-16

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.